Henry declared last week he expected a top four finish.
Carragher told the Sunday Mirror: "It's a big jump to go from sixth place to top spot, but if you don't believe in yourself at the start of the season then you never will. The supporters expect us to be up there challenging and I think the players should have that expectation too.
"It's harder to win the title now than it has ever been.
"Even finishing in the top four is tougher than ever now - as we've found out."